Two Stage Vehicle Routing Problem

Vehicle Routing Problem $($Model $4)$

Minimize ${\displaystyle \underset{k=1}{\overset{p}{}}}{\displaystyle \underset{i=1}{\overset{n}{}}}{\displaystyle \underset{j=1}{\overset{n}{}}}{T}_{ij}{x}_{\text{i}\text{j}\text{k}}$

Subject $to{\displaystyle \underset{k=1}{\overset{p}{}}}{\displaystyle \underset{i=1}{\overset{n}{}}}{x}_{\text{i}\text{j}\text{k}}=1,j=1,2,$dots,$n$

${\displaystyle \underset{k=1}{\overset{p}{}}}{\displaystyle \underset{j=1}{\overset{n}{}}}{x}_{\text{i}\text{j}\text{k}}=1,i=1,2,$dots,$n$

${\displaystyle \underset{i=1}{\overset{n}{}}}{D}_i{\displaystyle \underset{j=1}{\overset{n}{}}}{x}_{\text{i}\text{j}\text{k}}{C}_k,k=1,2,$dots,$p$

${\displaystyle \underset{i=1}{\overset{n}{}}}{x}_{\text{i}\text{l}\text{k}}-{\displaystyle \underset{j=1}{\overset{n}{}}}{x}_{ljk}=0,l=1,2,$dots,$n$;$k=1,2,$dots,$p$

$x_{\text{i}\text{j}\text{k}}=0or1,i,j=1,2,$dots,$n$;$k=1,2,$dots,$p$

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